Autocorrelated Errors Research Articles

Addressing Autocorrelation, Multicollinearity, and Heavy-Tail Errors in the Linear Regression Model

The most popular estimator for estimating parameters of linear regression models is the Ordinary Least Squares (OLS) Estimator. The OLS is considered the best linear unbiased estimator when certain assumptions are not violated. However, when autocorrelation, multicollinearity, and heavy-tail error are jointly present in the dataset, the OLS estimator is inefficient and imprecise. In this paper, we developed an estimator of linear regression model parameters that jointly handle multicollinearity, autocorrelation, and heavy tail errors. The new estimator, LADHLKL, was derived by combining the Hildreth-Lu (HL), the Kibria Lukman (KL), and the Least Absolute Deviation (LAD) estimators. The LADHLKL poses both the characteristics of the LAD, HL, and KL estimators which makes it resistant to both problems. We examined the properties of the proposed estimator and compared its performance with other existing estimators in terms of mean square error. An application to real-life data and simulation study revealed that the proposed estimator dominates other estimators in all the considered conditions in terms of mean square error.

A user-friendly method for estimating discrete choice land-use model in a panel data setting

Land-use modeling stands as a pivotal tool in shaping sustainable development policies. With the rapid advancement of remote-sensing technology and the widespread adoption of satellite imagery-based land cover products, these datasets have emerged as primary sources for understanding land-use dynamics due to their high spatial and temporal resolutions. Yet, it remains challenging to effectively integrate such rich panel data into nonlinear econometric land-use models. This paper introduces a method to seamlessly incorporate land cover panel data into econometric models, enabling comprehensive utilization of temporal information within a single framework.-By capturing dynamic land-use patterns, the method enhances prediction accuracy while mitigating issues such as autocorrelated error terms commonly encountered in panel data analysis.-The method is straightforward to implement and applicable to many nonlinear models, making it particularly suitable for datasets with large sample sizes.

An Efficient Way to Find Optimal Crossover Designs Using CVX for Precision Medicine

Crossover designs play an increasingly important role in precision medicine. We show the search of an optimal crossover design can be formulated as a convex optimization problem and convex optimization tools, such as CVX, can be directly used to search for an optimal crossover design. We first demonstrate how to transform crossover design problems into convex optimization problems and show CVX can effortlessly find optimal crossover designs that coincide with a few theoretical crossover optimal designs in the literature. The proposed approach is especially useful when it becomes problematic to construct optimal designs analytically for complicated models. We then apply CVX to find crossover designs for models with auto-correlated error structures or when the information matrices may be singular and analytical answers are unavailable. We also construct N-of-1 trials frequently used in precision medicine to estimate treatment effects on the individuals or to estimate average treatment effects, including finding dual-objective optimal crossover designs.

Adjustment for Neural Network Autocorrelation Error in Sequence Prediction based on Frequency Decomposition Algorithm

Adjustment for Neural Network Autocorrelation Error in Sequence Prediction based on Frequency Decomposition Algorithm

The impact of economic globalization on income inequality in middle-income countries in Asia: An empirical analysis from 2018 to 2021

This study investigates the relationship between economic globalization and income inequality in Asia during the period from 2018 to 2021. The research aims to contribute to the academic and policy debates on the impact of globalization on income inequality and to identify effective policy measures that can help mitigate the negative effects of globalization on income distribution in Asian countries. In this study, the relationship between income inequality and economic globalization is analyzed using the Random Effects Model (REM) and Generalized Least Squares (GLS) estimation to address the issues of auto-correlated errors and heteroscedasticity in the selected model. The study utilizes secondary data from the World Bank about 28 middle-income countries in Asia, spanning the period from 2018 to 2021, the International Monetary Fund, and the United Nations Development Program. The results of the study indicate that economic globalization is positively correlated with income inequality. The findings of this study provide insights and recommendations that can help policymakers, academics, and other stakeholders better understand the complex relationship between economic globalization and income inequality and identify strategies for promoting more equitable economic growth and development in Asia.

On the Performance of Some Estimation Methods in Models with Heteroscedasticity and Autocorrelated Disturbances (A Monte-Carlo Approach)

The proliferation of panel data studies has been greatly motivated by the availability of data and capacity for modelling the complexity of human behaviour than a single cross-section or time series data and these led to the rise of challenging methodologies for estimating the data set. It is pertinent that, in practice, panel data are bound to exhibit autocorrelation or heteroscedasticity or both. In view of the fact that the presence of heteroscedasticity and autocorrelated errors in panel data models biases the standard errors and leads to less efficient results. This study deemed it fit to search for estimator that can handle the presence of these twin problems when they co- exists in panel data. Therefore, robust inference in the presence of these problems needs to be simultaneously addressed. The Monte-Carlo simulation method was designed to investigate the finite sample properties of five estimation methods: Between Estimator (BE), Feasible Generalized Least Square (FGLS), Maximum Estimator (ME) and Modified Maximum Estimator (MME), including a new Proposed Estimator (PE) in the simulated data infected with heteroscedasticity and autocorrelated errors. The results of the root mean square error and absolute bias criteria, revealed that Proposed Estimator in the presence of these problems is asymptotically more efficient and consistent than other estimators in the class of the estimators in the study. This is experienced in all combinatorial level of autocorrelated errors in remainder error and fixed heteroscedastic individual effects. For this reason, PE has better performance among other estimators.

Spatial-Temporal Attention TCN-Based Link Prediction for Opportunistic Network

Link prediction for opportunistic networks faces the challenges of frequent changes in topology and complex and variable spatial-temporal information. Most existing studies focus on temporal or spatial features, ignoring ample potential information. In order to better capture the spatial-temporal correlations in the evolution of networks and explore their potential information, a link prediction method based on spatial-temporal attention and temporal convolution network (STA-TCN) is proposed. It slices opportunistic networks into discrete network snapshots. A state matrix based on topology information and attribute information is constructed to represent snapshots. Time convolutional networks and spatial-temporal attention mechanisms are employed to learn spatial-temporal information. Furthermore, to better improve link prediction performance, the proposed method converts the auto-correlation error into non-correlation error. On three real opportunistic network datasets, ITC, MIT, and Infocom06, experimental results demonstrate the superior predictive performance of the proposed method compared to baseline models, as shown by improved AUC and F1-score metrics.

Design of a novel intelligent computing framework for predictive solutions of malaria propagation model.

The paper presents an innovative computational framework for predictive solutions for simulating the spread of malaria. The structure incorporates sophisticated computing methods to improve the reliability of predicting malaria outbreaks. The study strives to provide a strong and effective tool for forecasting the propagation of malaria via the use of an AI-based recurrent neural network (RNN). The model is classified into two groups, consisting of humans and mosquitoes. To develop the model, the traditional Ross-Macdonald model is expanded upon, allowing for a more comprehensive analysis of the intricate dynamics at play. To gain a deeper understanding of the extended Ross model, we employ RNN, treating it as an initial value problem involving a system of first-order ordinary differential equations, each representing one of the seven profiles. This method enables us to obtain valuable insights and elucidate the complexities inherent in the propagation of malaria. Mosquitoes and humans constitute the two cohorts encompassed within the exposition of the mathematical dynamical model. Human dynamics are comprised of individuals who are susceptible, exposed, infectious, and in recovery. The mosquito population, on the other hand, is divided into three categories: susceptible, exposed, and infected. For RNN, we used the input of 0 to 300 days with an interval length of 3 days. The evaluation of the precision and accuracy of the methodology is conducted by superimposing the estimated solution onto the numerical solution. In addition, the outcomes obtained from the RNN are examined, including regression analysis, assessment of error autocorrelation, examination of time series response plots, mean square error, error histogram, and absolute error. A reduced mean square error signifies that the model's estimates are more accurate. The result is consistent with acquiring an approximate absolute error close to zero, revealing the efficacy of the suggested strategy. This research presents a novel approach to solving the malaria propagation model using recurrent neural networks. Additionally, it examines the behavior of various profiles under varying initial conditions of the malaria propagation model, which consists of a system of ordinary differential equations.

Temporal covariance of spatial soil moisture variations: A mechanistic error modeling approach

AbstractWhen estimating field‐scale average soil moisture from sensors measuring at fixed positions, spatial variability in soil moisture leads to “measurement errors” of the spatial mean, which may persist over time due to persistent soil moisture patterns resulting in autocorrelated measurement errors. The uncertainty of parameters that are derived from such measurements may be underestimated when they are assumed to be independent. Temporal autocorrelation models assume stationary random errors, but such error models are not necessarily applicable to soil moisture measurements. As an alternative, we propose a mechanistic error model that is based on the spatial variability of the water retention curve and assumes a uniform water potential. We tested whether spatial soil moisture variability and its temporal covariance could be predicted based on (1) mean soil moisture, (2) water retention variability, and (3) (co)variances of the van Genuchten parameters using a first‐order expansion of the retention curve. The proposed models were tested in a numerical and a field experiment. For the field experiment, in situ sensor measurements and water retention curves were obtained in a field plot. Both experiments showed that water retention variability under a uniform water potential is a good predictor for spatial soil moisture variability, and that soil moisture errors are strongly correlated in time and neglecting them would be an incorrect assumption. The temporal error covariance could be predicted as a function of the mean moisture contents at two observation times. Further research is required to assess the impact of these temporal correlations on soil moisture predictions.

Estimation of Cpm for autocorrelated data in the presence of random measurement errors

Process capability analysis is a widely used process improvement metric. There are several capability indices used in industries to assess the performance of production process. is one of the most important capability index which is often used in many industries for assessing the performance of the production process by taking into consideration the target value. Although capability indices are estimated under the assumption that the data are independent but in many industries, process outputs are often autocorrelated. At the same time, no measuring device gives accurate results. In this paper, we discuss the statistical properties of the estimator of for autocorrelated data and in the presence of random measurement errors. Here, we show that under the combined effect of autocorrelation and measurement errors, the estimator of behaves differently depending upon the variability of the measurement errors.

Bayesian Restricted Stein-rule Least Squares with non-spherical Disturbances

Bayesian restricted stein-rule least squares is a novelty estimator introduced to obtain parameters of the family of restricted least squares with intertwined heteroscedastic and autocorrelated disturbance errors. Errors in regression modelling set to measure the quality of the data and or model of which intertwining of most prominent errors disturbances play a significant role in determining the quality of the aforementioned. Efforts were geared towards the comparison of the performances and relative efficiency of the small sample property of Bayesian and classical family of restricted stein-rule least squares. The sample size was set at 25 to capture the intertwined disturbance errors, and the iteration of the Monte Carlo simulation was set at 10000 for both classical and Bayesian paradigms. and for both Autoregressive of order one (AR(1)) and Moving average of order one (MA(1)) processes respectively were set asymmetrically as -0.8,-0.5,-0.3, 0,0.3,0.5 and 0.8 while as a scale of heteroscedasticity was set at 0-homoscedasticity, -0.3-mild,-0.5-moderate and (0.7,0.9)-severe. The outcome of the study pointed out that Bayesian estimation (both posterior mean and Bayes estimates) for both restricted and restricted stein-rule estimators outperformed classical restricted and restricted stein-rule estimators in both performances and relative efficiency. It is therefore recommended to make use of the Bayesian framework when encountering similar disturbances in a small sample size.

Modelling and mapping Soil Organic Carbon in annual cropland under different farm management systems in the Apulia region of Southern Italy

Soil Organic Carbon (SOC) plays a crucial role in many soil functions and ecosystem services. Monitoring its spatial and temporal changes is essential for planning strategies to minimize soil degradation and loss and maintain its quality. Conservation Agriculture (CA) can make a significant contribution to increasing SOC. This article reports on the spatially modeled SOC concentration in the topsoil (0–0.3 m) of the Annual Cropland (ACL) under Conventional Management (CM) and CA in the Apulia region in Italy. To assess the spatial and temporal dynamics of SOC at the regional scale, the “Scorpan-SSPFe” (soil spatial prediction function with spatially autocorrelated errors) approach to predictive modeling and mapping of soil, based on the Geographically Weighted Regression (GWR) model was performed. The method was implemented using a Geographic Information System (GIS) and Google Earth Engine (GEE) environment to calculate the percentage distribution for each SOC level, altitude, and slope class and their combination. 80 environmental variables and 250 soil samples were analyzed to map the SOC in ACL. The SOC values showed an average of 16.68 and 17.73 g/kg for CM and CA respectively. Adequate map accuracy was obtained by GWR, which showed an R2 of 0.71 for CA and R2 of 0.52 for CM The Root Mean Squared Error (RMSE) predictions obtained were better in CA (3.96 g/kg) than CM (5.65 g/kg) with a percentage RMSE difference of 30 %. Predicted SOC obtained by GWR ranged from 4.06 to 35.60 g/kg for CA and from 5.00 to 29.99 g/kg for CM. The proposed method was shown to be promising in predicting SOC in a region of the Mediterranean area and can be used to assess the effect of land use changes, such as the application of CA, on SOC in the whole basin.

MWDINet: A multilevel wavelet decomposition interaction network for stock price prediction

Stock price prediction is a classical interdisciplinary issue drawn from finance, computer science, econometrics, and mathematics. Most stock price data are nonlinear, nonstationary, and highly complex, making stock price prediction challenging. Recently, deep neural networks (DNNs) have demonstrated powerful learning capabilities and have yielded notable results in stock price prediction tasks. Most existing deep learning solutions, however, only consider time-domain information or lack effective modeling of frequency-domain information, thus failing to effectively utilize both time-domain and frequency-domain information of the data. Meanwhile, existing methods ignore autocorrelated errors in the stock price forecasting task due to missing valid information data, i.e., they do not consider the correlation between the error at the current time step and the error at the previous time step, which undermines the standard maximum likelihood estimation (MLE) assumption, thereby weakening the model’s performance. We propose a multilevel wavelet decomposition interaction network (MWDINet), an end-to-end framework for stock price prediction. MWDINet employs the multiscale wavelet decomposition interaction module (MWDI-Block) and the Hull Moving Average module (HMA-Block) to extract the data’s frequency-domain and time-domain information, respectively. In MWDI-Block, the traditional signal processing method of Maximum Overlapping Discrete Wavelet Transform (MODWT) is seamlessly embedded into a deep learning framework (named DMODWT). The DMODWT algorithm not only automatically extracts the frequency-domain information from the data, but also fine-tunes the wavelet filters. With HMA-Block, we improve the Hull Moving Average (HMA), commonly used in the industry, into a deep learning module, which learns how changes in different markets over time. Inspired by the research on correcting autocorrelated errors in linear models in econometrics, we further design a deep difference module (DIF-Block) to correct autocorrelated errors and thus improve the prediction performance of the model. Moreover, all components are integrated seamlessly in a unified end-to-end framework. Extensive experiments on real-world datasets demonstrate that MWDINet outperforms the state-of-the-art models and has remarkable potential in stock price prediction.

Autocorrelated unreplicated linear functional relationship model for multivariate time series data

The conventional practices in handling cross-sectional data treated the explanatory variables as fixed variables without measurement errors. This article proposed a novel autocorrelated unreplicated linear functional relationship model (AULFR) model to accommodate the autocorrelated errors in the measurement errors model. Some basic properties of the model have been derived. A modified backshift operator is used in transforming the autocorrelated error into uncorrelated error. Simulation studies show that AULFR outperforms other benchmarking models even with a relatively small training data percentage or a sample size of 100 training observations. The application of the AULFR model on an actual economic case shows consistent results with simulation studies. The advantages of the proposed model are (i) it models the relationship between a time-based dependent variable and a set of time-based explanatory variables which subjected to measurement errors, and (ii) it can predict the current or future values of both dependent and explanatory variables using historical data.

Testing for financial bubbles in the presence of auto-correlated errors

How to detect financial bubble? In response to this question, a vast amount of empirical research is devoted spanning almost half-century. However, identifying unambiguously the presence of a bubble in the financial time series remains an unsolved problem in standard econometric and financial economic approaches. In this paper, we study the impact of auto-correlated innovations, which is a most common feature of the financial time series, on recently developed unit root tests with varying lag to detect financial bubbles. We apply the more powerful test procedure to identify bubble on the quarterly observations of house price-rent ratios of 4 counties. The results of the study suggest that rolling Max Supremum Augmented Dickey-Fuller (MSADF) test as the best test procedure to detect financial bubbles in the future.

Uncertainty, imperfect information, and expectation formation over the firm’s life cycle

Using a long panel data set on Japanese firms, we find that firms make more precise forecasts and less autocorrelated forecast errors as they gain more experience. Then, we build a firm dynamics model where firms gradually learn about their demand by using a noisy signal. Using expectations data over time, we cleanly isolate the learning mechanism from other mechanisms and find that it accounts for 20%–40% of the overall decline in forecast errors over the life cycle. Productivity gains from removing information frictions range from 3% to 12%, with firm entry and exit playing prominent roles.

Study of Jupiter’s Interior with Quadratic Monte Carlo Simulations

We construct models for Jupiter’s interior that match the gravity data obtained by the Juno and Galileo spacecraft. To generate ensembles of models, we introduce a novel quadratic Monte Carlo technique, which is more efficient in confining fitness landscapes than the affine invariant method that relies on linear stretch moves. We compare how long it takes the ensembles of walkers in both methods to travel to the most relevant parameter region. Once there, we compare the autocorrelation time and error bars of the two methods. For a ring potential and the 2d Rosenbrock function, we find that our quadratic Monte Carlo technique is significantly more efficient. Furthermore, we modified the walk moves by adding a scaling factor. We provide the source code and examples so that this method can be applied elsewhere. Here we employ our method to generate five-layer models for Jupiter’s interior that include winds and a prominent dilute core, which allows us to match the planet’s even and odd gravity harmonics. We compare predictions from the different model ensembles and analyze how much an increase in the temperature at 1 bar and ad hoc change to the equation of state affect the inferred amount of heavy elements in the atmosphere and in the planet overall.

Application of machine learning algorithms and Sentinel-2 satellite for improved bathymetry retrieval in Lake Victoria, Tanzania

Estimating bathymetric information is vital for aquaculture and navigation applications. Free, high-resolution satellite imagery provides a cost-effective solution for routine bathymetric measurements. We tested six algorithms to retrieve water depth in the Mwanza Gulf of Lake Victoria using Sentinel-2 satellite imagery: the conventional Stumpf method, Random Forest (RF), Gradient Boosting Machine (GBM), Extreme Gradient Boosting (XGB), Neural Network (NNET), and Support Vector Machine (SVM). In-situ depth points collected via echo sounders were used to train and validate the algorithms. Performance evaluation metrics included coefficient of determination (R2), mean absolute error (MAE), root-mean-square error (RMSE), and spatial autocorrelation of residuals. Among the algorithms tested, the Stumpf model exhibited moderate performance with an R2 of 0.441, higher MAE (2.078 m), and RMSE (2.964 m) values. The RF algorithm improved performance with an R2 of 0.957, lower MAE (0.476 m), and RMSE (0.823 m). The GBM and XGB algorithms achieved R2 values of 0.960 and 0.956, respectively, with low MAE (0.484 m for GBM, 0.482 m for XGB) and RMSE (0.795 m for GBM, 0.830 m for XGB) values. The NNET algorithm outperformed the GBM and XGB models, obtaining an R2 of 0.963, the lowest MAE (0.438 m), and RMSE (0.761 m). The SVM algorithm demonstrated the best performance with an R2 of 0.965, the lowest MAE (0.403 m), and RMSE (0.745 m), implying the highest accuracy in depth estimation. SVM also showed stable generalization across different locations with insignificant spatial autocorrelation of residuals. Therefore, SVM is recommended for repetitive bathymetry calculations.

Bayesian regularization networks for micropolar ternary hybrid nanofluid flow of blood with homogeneous and heterogeneous reactions: Entropy generation optimization

This study aims to analyze a Bayesian regularization backpropagation algorithm for micropolar ternary hybrid nanofluid flow over curved surfaces with homogeneous and heterogeneous reactions, Joule heating and viscous dissipation. The ternary hybrid nanofluid consists of nanoparticles of titanium oxide (TiO2), copper oxide (CuO), and silicon oxide (SiO2), with blood as the base fluid. The governing partial differential equations for the fluid flow are converted into ordinary differential equations using a group of self-similar transformations. The ordinary differential equations are solved using an appropriate shooting algorithm in MATLAB. The effects of physical parameters including curvature, micro-polar, radiation, magnetic, Prandtl, Eckert, Schmidt, and homogeneous and heterogeneous chemical reaction parameters are analyzed for velocity, micro rotational, temperature, and concentration profile. Physical quantities of engineering interest like heat transfer rate, mass transfer rate, skin friction coefficient, couple stress coefficient, and entropy generation are also discussed in this study. A Bayesian regularization backpropagation algorithm is also designed for the solution of the ordinary differential equations. The obtained network is analyzed using training state, performance, error histograms, model response, Error autocorrelation, and input-error correlation plots. It is observed that the entropy generation and the Bejan number increase for enhancing Brinkman and radiation parameter. Clinical researchers and biologists may use the results of this computational study to forecast endothelial cell damage and plaque deposition in curved arteries, by which the severity of these conditions can be reduced.

Improved environmental mapping and validation using bagging models with spatially clustered data

Spatially clustered sampling may result in non-independent data that pose challenges for environmental mapping applications. Two outstanding challenges resulting from the use of spatially clustered data for predictive geospatial modelling with machine learning approaches are biased model training and validation. These issues can be severe for popular bagging models such as Random Forest, yet one or both are often ignored or are handled using sub-optimal approaches. We propose to address these challenges using information on both the spatial autocorrelation of map errors and the spatial sampling intensity. This is achieved by applying the residual spatial covariance as a weighting function for the bagging procedure and for the calculation of weighted validation statistics. Using this approach, the full feature space of the sample data is retained during model training and validation. The utility of covariance weighting for these purposes is investigated through extensive simulation with a range of sample clustering configurations. Results are benchmarked against existing approaches. Covariance weighting improved model performance across a range of clustering scenarios but appeared to produce the greatest improvements for highly clustered data. Covariance-weighted validation demonstrated low bias across a broad range of clustering scenarios compared to existing spatial methods. Findings also suggest, though, that conditional Gaussian simulation approaches may perform well when the proportion of clustered data is very high. Covariance weighting is straightforward to implement, computationally efficient, and scales to different sample sizes and spatial extents.